Solid State Communications, Vol. 108, No. xx, pp. 1–6, 1998
c 1998 Elsevier Science Ltd. All rights reserved
0038–1098/98 $ - see front matter
Pergamon
PII: S0038–1098(98)00387-1
THE MAGNETIC STRUCTURES OF DyNi2 Ge2
Zahirul Islam a,1, C. Detlefs a,2 , A.I. Goldman a , S.L. Bud’ko a , P.C. Canfield a and A. Zheludev b
Laboratory and Department of Physics and Astronomy, Iowa State University, Ames, Iowa, IA
50011, U.S.A.
b
Department of Physics, Brookhaven National Laboratory, Upton, New York, NY 11973, U.S.A.
a Ames
(Received 21 July 1998; accepted 3 August 1998 by P. Burlet)
In this paper we report the results of neutron diffraction measurements
of the magnetic structures of a single crystal of DyNi2 Ge2 in zero applied magnetic field. There are two distinct magnetic transitions in this
material; one is from the paramagnetic phase to an amplitude modulated
(AM) antiferromagnetic phase at the Néel temperature, TN = 8.3±0.1
K, and the other is at a lower temperature, Tt = 3.1±0.2 K, from this
phase to an equal moment (EM) antiferrromagnetic structure. The EM
structure is described by a set of three wave vectors, namely, τ1 = (0
0 34 ), τ2 = ( 21 12 0) and τ3 = ( 12 21 12 ). A weak third harmonic, τ10 = (0
0 14 ), related to τ1 , also appears indicating that the magnetic structure
is not purely sinusoidal. In this phase Dy moments have their full saturation value of µs = 10 µB . The AM phase is described by a single
propagation vector τ1 . In both the phases there is an ordered component of the Dy moments in the basal plane. The angle between the ordered Dy moments and the the ĉ axis is estimated to be 17◦ ±6◦ at 1.5
K. These results are consistent with the dc susceptibility as a function
of temperature data which shows weak anisotropy and two transitions.
c 1998 Elsevier Science Ltd. All rights reserved
Keywords: A. Magnetically ordered materials, D. Phase transitions,
E. Neutron scattering.
1. INTRODUCTION
materials have been performed on polycrystalline samples where the valuable information about anisotropy
was lost due to powder averaging. Recently, high quality single crystals of these materials have been grown
in Ames Laboratory using a high-temperature-fluxgrowth [2] technique and their magnetic and electronic
transport properties as a function of rare earth component have been studied in detail. [3]
As a part of this series-wide study we have carried out a complete determination of the zero field
magnetic structures of TbNi2 Ge2 using both neutron
diffraction and X-ray resonant exchange scattering
(XRES) techniques. [4] In addition, XRES studies of
GdNi2 Ge2 and EuNi2 Ge2 magnetic structures have
also been performed which will be published elsewhere. [5] The present work is concerned with the
zero field magnetic structures of another member of
In the study of the interplay between long range magnetic order and single-ion anisotropy in rare earth intermetallic compounds, tetragonal systems offer distinct advantages. Many of these systems are either uniaxial or planar in their anisotropic magnetic behaviors.
This anisotropy is primarily determined by the crystal
elecric field (CEF) splittings of the Hund’s rule ground
state J multiplet which, in tetragonal systems, requires
only a few parameters to be specified. The RNi2 Ge2
family is such a system. Its magnetic properties are
similar to those of the RNi2 Si2 series which exhibits
considerable magneto-crystalline anisotropy. [1] Until recently, however, bulk measurements on RNi2 Ge2
1
2
E-mail: zahirul@iastate.edu
Present Address: ESRF, Grenoble, France.
1
2
THE MAGNETIC STRUCTURES OF DyNi2 Ge2
this family, DyNi2 Ge2 , which will provide a starting
point for future investigations of the field induced
structures mentioned below.
DyNi2 Ge2 crystallizes in the body centered tetragonal ThCr2 Si2 structure [6] with space group I4/mmm
(for details see Ref. [4]). The magnetic properties of
this material have been studied by various groups.
The ordering temperature of 11 K reported by earlier groups [7, 8] is considerably different than those
found by André and co-workers who have carried out
a detailed study on polycrystalline DyNi2 Ge2 sample. [9] They observed a paramagnetic to an antiferromagnetic phase transition at TN = 7.5 K in their
susceptibility measurement. According to their powder neutron diffraction measurements, this transition
takes place at 8.5 K. Using neutron diffraction methods on powder sample they found the ordered phase,
at 1.4 K, to be an incommensurate sinusoidally amplitude modulated (AM) structure with propagation vector (0 0 0.788). Further, they found that the ordered
Dy moments form an angle of 20◦ with the ĉ axis.
As shown below the transition temperatures and, the
propagation vectors are significantly different in high
quality single crystals.
High quality single crystals of DyNi2 Ge2 were
grown at Ames Laboratory using a high-temperatureflux-growth technique. [2] X-ray powder diffraction
pattern confirmed the room temperature structure to
be of the ThCr2 Si2 type with no evidence of second
phases. The anisotropic magnetization was measured
using a Quantum Design MPMS-5 SQUID magnetometer which provides a temperature range of 1.8
K–350 K and a magnetic field upto 55 kG.
The neutron scattering measurements on a single
crystal of DyNi2 Ge2 were carried out at the H4M
spectrometer of High Flux Beam Reactor (HFBR) at
Brookhaven National Laboratory. Neutrons with energies of 14.7 meV were used with collimator settings
of 400 -400 -800 -none. Pyrolytic graphite filters were
used to eliminate second harmonic ( λ2 ) contamination
of the beam. No special preparation of the sample was
necessary. The largest crystal of the same batch used
for the magnetization measurements was chosen. The
sample was closely a square plate with dimensions of
7 mm×7 mm×1.5 mm and weighing about 300 mg.
2. MAGNETIZATION
The temperature dependence of the low field susceptibility with applied field parallel (H k ĉ) and perpendicular (H ⊥ ĉ) to the ĉ axis was found to be
anisotropic. From cusps in the susceptibility two transitions were identified, and are indicated in Fig. 1(a).
Vol. 108, No. xx
The paramagnetic to antiferromagnetic transition occurs at TN = 8.2 K. The second transition is at a lower
temperature, Tt = 3.2 K. This is in contrast to previous
susceptibility measurement [9] where only one transition at TN = 7.5 K was observed. This may be a consequence of polycrystalline averaging which often makes
the lower transition less pronounced as was found to
happen in GdNi2 B2 C (see Ref. [10]). In this material
a second transition at 14 K (the Néel temperature is
20 K) due to the Gd spin reorientation was observed
using XRES. [11] Such subtle transitions are particularly difficult to detect in a polycrystalline sample.
The magnetization as a function of field applied
along the ĉ axis at 2 K (Fig. 1(b)) shows two metamagnetic transitions at 18 kG and 27 kG respectively.
We believe that on further lowering of the temperature these transitions would become sharper (similar
to data in Ref. [4]) with the appearence of at least one
more transition approximately at 9 kG which is barely
discernible at this temperature Also since the moment
does not acquire the full saturation value of 10 µB up
to 55 kG it is conceivable that there may be one or
more metamagnetic transitions in higher fields. When
the field is in the basal plane, however, the magnetization does not manifest any transitions.
This magnetic behavior is very similar to that of the
isostructural DyNi2 Si2 compound. [12–14] This material has two magnetic phase transitions, at 3.4 K and
6 K, respectively. As in DyNi2 Ge2 , the anisotropy is
not very strong. At 1.5 K, there are four metamagnetic transitions with field applied along the ĉ axis. [12]
This behavior was found to be qualitatively like that
of TbNi2 Si2 . [15] The zero field magnetic structures in
these two materials were found also to be quite similar. [13, 16]
Interestingly, the magnetic behavior of DyNi2 Ge2
is also qualitatively similar to that of the neighboring
member of the series, TbNi2 Ge2 , which exhibits two
magnetic transitions, [3, 4] at TN = 16.8 K and Tt =
9.3 K, respectively, in zero field. The magnetization
measurements on this material at 2 K with the field
parallel to the ĉ axis shows a sequence of five metamagnetic transitions below 55 kG. Both the susceptibilty and magnetization showed strong anisotropy
with the ĉ axis as the easy axis of magnetization. Neutron and XRES measurements showed indeed the ordered moments are aligned with the ĉ axis. This material was shown to be a good candidate for the study of
metamagnetic phase transitions and possibly “devil’s
staircase” (see Ref. [17]) type behavior. In the case
of DyNi2 Ge2 the anisotropy is not as strong as in
TbNi2 Ge2 . This implies that there may be ordered
component of Dy moments in the basal plane. Also,
Vol. 108, No. xx
THE MAGNETIC STRUCTURES OF DyNi2 Ge2
3
Fig. 1. (a) Susceptibility and (b) magnetization of
DyNi2 Ge2 single crystal. The dashed vertical lines in
(a) indicate the positions of the transition temperatures, TN and Tt , respectively.
as mentioned above, the metamagnetic phase transitions in DyNi2 Ge2 may become sharper as the temperature is lowered below 2 K making this material
another system for the study of metamagnatism.
3. NEUTRON DIFFRACTION
MEASUREMENTS
For our neutron diffraction measurements, a single crystal of DyNi2 Ge2 was aligned in the [H H L]
zone. At 11 K, well above TN determined from the susceptibility data, scans along various symmetry directions in this zone showed only nuclear peaks consistent
with the body centered tetragonal crystal structure (i.e.
H+K+L = 2n where n is an integer) with lattice parameters a = 4.031±0.003 Å and c = 9.776±0.004 Å at
this temperature. No significant variations of the lattice parameters with temperature were observed. Below TN , magnetic satellite peaks corresponding to τ1
= (0 0 34 ) developed. The presence of weak magnetic
satellites of (0 0 L) associated with τ1 indicated that
there is a small component of the ordered moments in
the basal plane perpendicular to the ĉ axis.
At 1.5 K, below the second transition at Tt , additional superlattice peaks associated with τ2 = ( 12 21 0)
Fig. 2. Selected reciprocal lattice scans at 1.5 K in the
[H H L] zone showing various magnetic peaks. (a) [ 32 32
L] scan, (b) [1 1 L] scan and (c) [0 0 L] scan. The small
peaks at 2.5 and 3.6 in (c) are from a second grain in
the sample. The τ10 satellites in the [0 0 L] scan were
too weak to be observed. Note that the intensities are
shown on logarithmic scales.
and τ3 = ( 12 21 21 ) emerged (see Fig. 2(a)). A third harmonic, τ10 = (0 0 14 ), related to τ1 also developed indicating a squaring up of the structure. ∗ No other
modulations in this zone were found. Again, the presence of relatively weak τ and τ10 satellites of (0 0 L)
nuclear peaks imply a small component of the ordered
moments in the basal plane. The magnetic unit cell of
this structure consists of 16 chemical unit cells as implied by the simultaneous existence of τ1 and τ2 .
The integrated intensities of various magnetic Bragg
peaks corresponding to (1 1 2)-τ1 , (1 1 2)-τ10 , (1 1
2)+τ2 and (2 2 2)-τ3 are shown in Fig. 3 as a function
∗ Here we mention that our definition of a propagation vector
is made with respect to the center (Γ ) of the Brillouin zone (BZ)
which has the full point group symmetry of the space group of
the underlying crystal structure. Then the third harmonic of τ1 =
(0 0 34 ) is 3τ1 which is τ10 = (0 0 14 ) when reduced to the first BZ.
4
THE MAGNETIC STRUCTURES OF DyNi2 Ge2
of temperature. The intensity of τ1 satellite increases
continuously from zero at TN and has a small break
at the lower phase transition at Tt . Below this temperature, magnetic peaks corresponding to τ2 and τ3 appear. Both τ2 and τ3 show very similar dependencies
on temperature which suggests that these modulation
vectors are related. The third harmonic becomes negligibly small above Tt indicating that the structure in
this phase is essentially sinusoidal. As Tt is approached
from above, the structure starts to square up giving
rise to the harmonic.
The temperature dependence of these order parameters can be modeled by Brillouin type functions,
BJ (| T − Tc |) where Tc is the transition temperature,
shown by the solid lines in Fig. 3. In the case of the
15
τ1 order parmeter, J = 2 was used whereas for τ2
1
and τ3 , J = 2 was used. The transition temperatures
thus obtained are TN = 8.3±0.1 K and Tt = 3.1±0.2
K, in close agreement with those determined by susceptibility measurements. The fact that, below Tt , the
τ2 and τ3 order parameters can be modeled by BJ = 1
2
suggests that the CEF ground state is a magnetic
doublet. This is possible since Dy3+ is a Kramers ion.
3+ will always
The CEF split J = 15
2 multiplet of Dy
be at least doubly degenerate in the absence of an
external magnetic field. ∗ In the case of DyNi2 Si2
the magnetic entropy reaches ∼ R ln(10.7) at 30 K
which suggests that the CEF level scheme contains
at least five doublets within 50 K. [12] Due to the
isostructural relationship and similar magnetic behavior with this compound a similar set of CEF levels in
DyNi2 Ge2 seems feasible. In the temperature region
below Tt only the low lying CEF levels are important
due to thermal depopulation of the higher excited
levels. Since more CEF eigenstates are likely to be
involved above Tt , the temperature dependence of τ1
is different than those of τ2 and τ3 below Tt .
Also, in the case of the τ1 order parameter below Tt ,
there is a small enhancement of the intensity above that
expected from the Brillouin function behavior. This
is due to the Dy ions acquiring their full saturation
value of 10 µB upon going through the transition at
Tt from an AM structure above this temperature. If
the structure remained AM below Tt then the break
as shown in Fig. 3 is not expected.
The magnetically ordered phases of DyNi2 Ge2
are very similar to those found in the neighboring,
∗
The DJ= 15 manifold of Dy3+ ion reduces to even dimen2
sional representations of the D4h point group as follows:
Γ6−
Γ7−
DJ= 15 = 4Γ6− ⊕ 4Γ7−
2
where
and
are the odd irreducible representations of the
double group. See [18].
Vol. 108, No. xx
Fig. 3. Temperature dependence of various magnetic
reflections measured by neutron diffraction (Eneutron =
14.7 meV) on a single crystal. The arrow shows the
break in the τ1 order parameter. The intensities of τ10
was multiplied by 10 and those of τ2 and τ3 satellites
were multiplied by 5. Data were collected on raising
the temperature. The vertical dashed lines locate the
positions of the transition temperatures, TN and Tt ,
respectively.
isostructural, TbNi2 Ge2 compound. [4] This material orders below 16.8 K (TN) in an AM longitudinal
structure with propagation vector τ ≈ (0 0 0.758)
whereas below 9.3 K (Tt ) the structure becomes equal
moment (EM) commensurate with the same set of
modulation vectors (τ1 , τ10 , τ2 , τ3 ) as was found in
DyNi2 Ge2 below 3.2 K. The transition from the AM
to an EM structure in TbNi2 Ge2 was also evidenced
by the break and increase in intensity, of the τ1 satellite at Tt . Unlike the Tb compound, where the ordered
moments in both the phases are along the ĉ axis, there
is a component of Dy moments in the basal plane,
consistent with the susceptibility and low temperature
magnetization measurements.
4. MAGNETIC STRUCTURES AND
DISCUSSION
Based on our results, and the isostructural relationship to TbNi2 Ge2 , a magnetic structure as shown in
Fig. 4 for DyNi2 Ge2 below Tt = 3.1 K seems feasible. In this EM phase all the Dy moments have their
full saturation moment of 10 µB (consistent with the
Vol. 108, No. xx
THE MAGNETIC STRUCTURES OF DyNi2 Ge2
Fig. 4. The magnetic unit cell of DyNi2 Ge2 crystal
below Tt = 3.1 K. The ↑ (↓) represents the magnetic
moment of Dy atoms (solid circles). Ni and Ge atoms
have been omitted. The planes are numbered for reference.
Hund’s rule ground state, 6 H 15 ) aligned at an angle β
2
with respect to the ĉ axis. This structure consists of
antiferromagnetically coupled, ferromagnetically ordered, Dy planes forming triplets (planes #0–#2 and
#5–#7). Since two such neighboring triplets have opposite phases, the moments on planes #3 and #7 are
‘frustated’ which can lead to antiferromagnetic ordering in these planes. This element of frustration can
give rise to magnetic peak broadening below Tt as
was observed to occur with high resolution XRES in
TbNi2 Ge2 compound. [4] Due to extinction, shape and
absorption effects in the neutron diffraction measure-
5
ments on a single crystal sample, a precise determination of the tilt angle β at this temperature could not
be carried out. However, a rough estimate is β = 17◦
± 6◦ . Neutron diffraction from powdered single grains
sample is clearly needed for a better determination of
β. Due to the high neutron absorption cross section
of Dy (σa = 940 barns, see Ref. [19]), however, a better technique in this case is XRES on a single crystal
sample for the moment direction determination as has
been done in the GdNi2 B2 C, SmNi2 B2 C, NdNi2 B2 C
and TbNi2 Ge2 compounds (see Refs [4, 11, 20]).
The magnetic structure above Tt but below TN is a
sinusoidally AM structure described by a single propagation vector, τ1 , with no antiferromagnetic planes.
The ordered moments are at an angle β from the ĉ
axis. It is not clear if this β is different than that in
the EM phase. The ordering scheme in DyNi2 Ge2 just
described is like that in DyNi2 Si2 . [12, 14] The magnetic structure of DyNi2 Si2 below TN = 6 K but above
Tt = 3.7 K is sinusoidaly AM. Below Tt , the structure becomes EM commensurate. It is surprising, however, unlike the magnetic structures in DyNi2 Ge2 , the
ordered moments in DyNi2 Si2 are aligned with the
ĉ axis in both the phases although the magnetocrystalline anisotropies in both the materials are comparable. On the other hand, TbNi2 Ge2 and TbNi2 Si2
are strongly anisotropic with the ordered Tb moments
strictly aligned with the ĉ axis. [4, 16]
The magnetic orderings in the three compounds
TbNi2 Ge2 , TbNi2 Si2 and DyNi2 Si2 , respectively, have
two features in common. Below the respective ordering temperature, TN , they all order in a long period
AM structure. On further reducing the temperature
the AM structure locks-into the lattice becoming EM
commensurate at a lower transition temperatrue, Tt .
Due to the similar magnetic behavior of DyNi2 Ge2 , in
particular with that found in TbNi2 Ge2 , we expect the
modulation vector below TN to be slightly different
from (0 0 34 ) found in the present neutron diffraction
study, which implies a longer period of modulation as
is the case in the other materials above Tt but below
TN . The high resolution available to XRES measurements should be utilized in order to determine τ1 more
precisely.
We point out that due to the four-fold symmetry of
the tetragonal basal plane the possibility of a spiral
antiferromagnetic structure can not be ruled out. If,
however, there is an in-plane easy direction of magnetization one way to search for it is to measure the angular dependence of dc magnetization (see Ref. [21])
within the basal plane. Similarly, one can try to determine β in the paramagnetic phase if the anisotropy is
solely due to CEF effects. Such measurements to look
6
THE MAGNETIC STRUCTURES OF DyNi2 Ge2
for any such in-plane easy direction as well as to determine β are planned. In addition, the difference between a collinear EM structure and a spiral one can
also be determined with X-rays as well, using circularly polarized light (see Ref. [22, 23]).
Finally, the Néel transition temperature determined
from our neutron diffraction measurements is in agreement with that from our susceptibility measurements
and also with the one found in the earlier neutron
work on a polycrystalline sample. [9] However, our results are inconsistent with the value of τ1 = (0 0 0.788)
found by the previous workers. [9] The τ2 and τ3 satellites were not detected in the earlier work on a powder sample because they are very weak and Dy has a
very large absorption cross section (see above). However, the large discrepancy of τ1 can not be explained
so easily. Although strains induced by grinding process can change the modulation, it is surprising that
this could happen without significantly affecting TN .
An independent measurement using XRES can help
resolve this discrepancy.
Acknowledgements—Ames Laboratory (U.S. Department of Energy) is operated by Iowa State University
under Contract No. W-7405-Eng-82. This work was
supported by the Director for Energy Research, Office of Basic Sciences. The work at Brookhaven Narional Laboratory was carried out under Contract No.
DE-AC-0298CH10886, Division of Materials Science,
U.S. Department of Energy.
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